Essentially you craft the treadmill using an expensive recipe, similar to the parts of the cloning machine, and at the end you create a treadmill. When on this treadmill it speeds up the breeding process. It should be faster than flying on a pokemon or using speed potions. The recipe MUST be expensive too.
It will also be affected by Flame Body. It should also work on multiple eggs at once.
It would work like a mount and just make treadmill noises while you AFK or watch. No need for a fancy animation.